To find the sum of \( \frac{3}{4} \) and \( -\frac{11}{4} \), we can add the two fractions since they have a common denominator:
\[ \frac{3}{4} + \left( -\frac{11}{4} \right) = \frac{3 - 11}{4} \]
Calculating the numerator:
\[ 3 - 11 = -8 \]
So, we have:
\[ \frac{3}{4} + \left( -\frac{11}{4} \right) = \frac{-8}{4} \]
Now, we can simplify \( \frac{-8}{4} \):
\[ \frac{-8}{4} = -2 \]
Thus, the sum of \( \frac{3}{4} \) and \( -\frac{11}{4} \) is:
\[ \boxed{-2} \]